Yes. Migraine is caused by variations to the genes that relate to how ions are processed in the brain. So far 44 different loci have been identified as being related to migraine. Some people have a single gene variation, but most people have a combination of gene variations. It is strongly hereditary (if you have migraine there's a 50% chance your child will too), but because it is caused by a combination of genes in most people, you can still get it if your parents don't have it by getting some from mum, and some from dad. These genetic differences generally make the ions go too fast in a migraine brain, and that makes the migraine brain hyper-reactive to sensory inputs and other stimuli.
Learn more about migraine genetics